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Bridging the Gap: A Generalized Stochastic Process for Count Data

Author

Listed:
  • Li Zhu
  • Kimberly F. Sellers
  • Darcy Steeg Morris
  • Galit Shmueli

Abstract

The Bernoulli and Poisson processes are two popular discrete count processes; however, both rely on strict assumptions. We instead propose a generalized homogenous count process (which we name the Conway–Maxwell–Poisson or COM-Poisson process) that not only includes the Bernoulli and Poisson processes as special cases, but also serves as a flexible mechanism to describe count processes that approximate data with over- or under-dispersion. We introduce the process and an associated generalized waiting time distribution with several real-data applications to illustrate its flexibility for a variety of data structures. We consider model estimation under different scenarios of data availability, and assess performance through simulated and real datasets. This new generalized process will enable analysts to better model count processes where data dispersion exists in a more accommodating and flexible manner.

Suggested Citation

  • Li Zhu & Kimberly F. Sellers & Darcy Steeg Morris & Galit Shmueli, 2017. "Bridging the Gap: A Generalized Stochastic Process for Count Data," The American Statistician, Taylor & Francis Journals, vol. 71(1), pages 71-80, January.
    • Handle: RePEc:taf:amstat:v:71:y:2017:i:1:p:71-80
    DOI: 10.1080/00031305.2016.1234976
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    Cited by:

    1. Born, Alexander & Kovachka, Nikoleta & Lessmann, Stefan & Seow, Hsin-Vonn, 2018. "Price Management in the Used-Car Market: An Evaluation of Survival Analysis," IRTG 1792 Discussion Papers 2018-065, Humboldt University of Berlin, International Research Training Group 1792 "High Dimensional Nonstationary Time Series".
    2. Kimberly F. Sellers & Andrew W. Swift & Kimberly S. Weems, 2017. "A flexible distribution class for count data," Journal of Statistical Distributions and Applications, Springer, vol. 4(1), pages 1-21, December.
    3. Geng, Xi & Xia, Aihua, 2022. "When is the Conway–Maxwell–Poisson distribution infinitely divisible?," Statistics & Probability Letters, Elsevier, vol. 181(C).
    4. Valdés, Rosa Maria Arnaldo & Comendador, Victor Fernando Gómez & Castán, Javier Alberto Perez & Sanz, Alvaro Rodriguez & Sanz, Luis Perez & Ayra, Eduardo Sanchez & Nieto, Francisco Javier Saez, 2019. "Development of safety performance functions (SPFs) to analyse and predict aircraft loss of separation in accordance with the characteristics of the airspace," Reliability Engineering and System Safety, Elsevier, vol. 186(C), pages 143-161.
    5. Kimberly F. Sellers & Ali Arab & Sean Melville & Fanyu Cui, 2021. "A flexible univariate moving average time-series model for dispersed count data," Journal of Statistical Distributions and Applications, Springer, vol. 8(1), pages 1-12, December.

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